Interpretive Summary: Objective measures are needed to quantify dietary adherence during caloric restriction (CR) while participants are freeliving. One method to monitor adherence is to compare observed weight loss to the expected weight loss during a prescribed level of CR. Normograms (graphs) of expected weight loss can be created from mathematical modeling of weight change to a given level of CR, conditional on the individual’s set of baseline characteristics. These normograms can then be used by counselors to help the participant adhere to their caloric target. The purposes of this study were to develop models of weight loss over a year of caloric restriction and to utilize these models to develop normograms, given the level of caloric restriction prescribed, and measures of these variables. Seventy-seven individuals completing a 6 - 12-month caloric restriction intervention (CALERIE) at three sites had body weight and body composition measured frequently. As expected, CR was quantitatively related to change in body weight. Using these estimates, different normograms for the weight change associated with female and male were developed. There are several limitations: Sample sizes are small, the protocols for the interventions differed by site, and not all subjects completed a year of follow-up. In addition, the inclusion of subjects by age and initial BMI was constricted, so that these results may not generalize to other populations including older and obese subjects.

Technical Abstract:
Objective measures are needed to quantify dietary adherence during caloric restriction (CR) while participants are freeliving. One method to monitor adherence is to compare observed weight loss to the expected weight loss during a prescribed level of CR. Normograms (graphs) of expected weight loss can be created from mathematical modeling of weight change to a given level of CR, conditional on the individual’s set of baseline characteristics. These normograms can then be used by counselors to help the participant adhere to their caloric target. The purposes of this study were 1) To develop models of weight loss over a year of caloric restriction given demographics, and well-defined measurements of body mass index, total daily energy expenditure (TDEE) and %CR; (2) To utilize these models to develop
normograms, given the level of caloric restriction prescribed, and measures of these
variables. Seventy-seven individuals completing a 6 - 12-month caloric restriction
intervention (CALERIE) at three sites (Pennington Biomedical Research Center, Tufts
University, and Washington University) had body weight and body composition measured frequently. Energy intake (and %CR) was estimated from TDEE (by doubly labeled water) and body composition (by DXA) at baseline and months 1, 3, 6, and 12. Bodyweight was modeled to determine the predictors and distribution of the expected trajectory of percent weight change over 12 months of CR. Results As expected, CR was related to change in body weight. Controlling for time-varying measures, initially simple models of the functional form indicated that the trajectory of percent weight change was predicted by a nonlinear function of age, TDEE, %CR, and sex. Using these estimates, normograms for the weight change were developed. Our model estimates that the mean weight loss (% change from baseline weight) for an individual adherent to a 25% CR regimen is _10.9_6.3% for females and _13.9þ6.4% for men after 12 months. There are several limitations: Sample sizes are small (n¼77), and, by design, the protocols, including prescribed CR, for the interventions differed by site, and not all subjects completed a year of follow-up. In addition, the inclusion of subjects by age and initial BMI was constricted, so that these results may not generalize to other populations including older and obese subjects. The trajectory of percent weight change during CR interventions in the presence of well-measured covariates can be modeled using simple nonlinear functions, and is related to level of CR, the percent change in TDEE, gender, and age.